## Optimal Coding and Sampling of Triangulations (2003)

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### BibTeX

@INPROCEEDINGS{Poulalhon03optimalcoding,

author = {Dominique Poulalhon and Gilles Schaeffer},

title = {Optimal Coding and Sampling of Triangulations},

booktitle = {},

year = {2003},

pages = {1080--1094},

publisher = {Springer}

}

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### Abstract

Abstract. We present a simple encoding of plane triangulations (aka. maximal planar graphs) by plane trees with two leaves per inner node. Our encoding is a bijection taking advantage of the minimal Schnyder tree decomposition of a plane triangulation. Coding and decoding take linear time. As a byproduct we derive: (i) a simple interpretation of the formula for the number of plane triangulations with n vertices, (ii) a linear random sampling algorithm, (iii) an explicit and simple information theory optimal encoding. 1